Language

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

Add and Subtract Fractions with Different Denominators: example 4.76 · Physics Playground

Exercises Numbers, fractions and percents

Example 4.76 from Prealgebra, 4.5 Add and Subtract Fractions with Different Denominators

Add and Subtract Fractions with Different Denominators: example 4.76

Simplify: $\frac{\frac{1}{2} + \frac{2}{3}}{\frac{3}{4} - \frac{1}{6}} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

	$\frac{\frac{1}{2} + \frac{2}{3}}{\frac{3}{4} - \frac{1}{6}}$
Rewrite numerator with the LCD of 6 and denominator with LCD of 12.	$\frac{\frac{3}{6} + \frac{4}{6}}{\frac{9}{12} - \frac{2}{12}}$
Add in the numerator. Subtract in the denominator.	$\frac{\frac{7}{6}}{\frac{7}{12}}$
Divide the numerator by the denominator.	$\frac{7}{6} \div \frac{7}{12}$
Rewrite as multiplication by the reciprocal.	$\frac{7}{6} \cdot \frac{12}{7}$
Rewrite, showing common factors.	$\frac{7 \cdot 6 \cdot 2}{6 \cdot 7 \cdot 1}$
Simplify.	2

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: $\frac{\frac{1}{3} + \frac{1}{2}}{\frac{3}{4} - \frac{1}{3}}$ .

How did it go?

PreviousAdd and Subtract Fractions with Different Denominators: example 4.75 Next Add and Subtract Fractions with Different Denominators: example 4.77

From Prealgebra (1st edition) by OpenStax (Rice University), section 4.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.